A Retrograde Approximation Algorithm for One-Player Can't Stop

Abstract. A one-player, finite, probabilistic game with perfect information can be presented as a bipartite graph. For one-player Can't Stop, the graph is cyclic and the challenge is to determine the game-theoretical values of the positions in the cycles. In this article we prove the existence and uniqueness of the solution to one-player Can't Stop, and give an efficient approximation algorithm to solve it by incorporating Newton's method with retrograde analysis. We give results of applying this method to small versions of one-player Can't Stop.

• Type: Conference
• Year: 2006
• Where: CG
• Authors: James Glenn, Haw-ren Fang, Clyde P. Kruskal
• Keywords: Bipartite Graph, CG 2006, Computer Graphics, Efficient Approximation Algorithm, Game-theoretical Values